1. Field of the Invention
The present invention relates to a gain-controlled amplifier the gain of which varies exponentially in response to a linear voltage variation of a control voltage applied to the amplifier, to operate with reduced distortion.
2. Description of the Prior Art
One typical circuit arrangement of conventional gain-controlled amplifiers is shown in FIG. 1, wherein the gain-controlled amplifier comprises: a first pair of bipolar transistors 1a and 1b (PNP type), a second pair of bipolar transistors 2a and 2b (NPN type), and an operational amplifier 3. The first pair of bipolar transistors 1a and 1b and the second pair of bipolar transistors 2a and 2b are designated by reference numerals 1 and 2, respectively. The emitters of transistors 1a and 1b are connected together to form a first common emitter, while the emitters of transistors 2a and 2b are also connected together to form a second common emitter. An input signal vi applied to an input signal terminal 4 is fed through respective resistors 5 and 6 having the same value of R.sub.1 to the respective first and second common emitters. A control voltage Vc from a control input terminal 11 is supplied to the bases of the transistors 1b and 2b, while the bases of the transistors 1 a and 2a are connected to ground. Constant current sources 8 and 10 supplies constant currents I.sub.1 and I.sub.2 to the first and second common emitters from power supply terminals 7(+Vcc) and 9(-Vcc), respectively. The collectors of the transistors 1a and 2b are coupled together and connected to ground, and the collectors of the transistors 1b and 2a are connected to an inverting input terminal of the operational amplifier 3, the non-inverting input terminal thereof being grounded. A feedback resistor 13 having a value of R.sub.2 is connected between the inverting input terminal and the output terminal of the operational amplifier 3. In this circuit, at a signal output terminal 12 is derived an output voltage V.sub.0 converted from a current i.sub.0 which is derived from the connection point of the collectors of the transistors 1b and 2a.
In the conventional gain-controlled amplifier with such a circuit configuration, the following relation is recognized between each emitter current i.sub.1 a, i.sub.1 b, i.sub.2 a and i.sub.2 b of the respective transistors 1a, 1b, 2a and 2b and the control voltage Vc, when the characteristics of the PN junction of the transistor are taken into account. ##EQU1## where K=q/kT, k represents a Boltzmann's constant, q represents an electric charge, and t represents a junction temperature. Assuming that the voltage vi of the input signal applied to the input terminal 4 is greater than each base-emitter voltage of the transistors 1a, 1b,2a and 2b, then the following equation may be derived. ##EQU2## By combining the two above equations (1) and (2) together, i.sub.1 b and i.sub.2 a are given by ##EQU3## The current i.sub.0 which is derived from either the transistor 1b or the transistor 2a and thereafter delivered to the operational amplifier 3 may be expressed by EQU i.sub.0 =i.sub.1 b-i.sub.2 a (4)
By substituting the equation (3) into the equation (4), then ##EQU4## The output voltage v.sub.0 appearing at the signal output terminal 12 may be expressed as EQU v.sub.0 =-i.sub.0 .multidot.R.sub.2 ( 6)
By substituting the equation (5) into the equation (6) above, then ##EQU5## Therefore, the voltage gain Av of the gain-controlled amplifier shown in FIG. 1 is expressed by the following equation. ##EQU6## From the above equation (8), it is understood that the voltage gain Av varies exponentially with the control voltage Vc, provided that the value of exp (K.multidot.Vc) in the divisor is larger than 1, that is, the control voltage Vc is larger than 0.
Such a gain-controlled amplifier as shown in FIG. 1 has been found, however, not entirely satisfactory. Disadvantages accompanied by such a gain-controlled amplifier as shown in FIG. 1 are that (1) since the gain-controlled amplifier is essentially so implemented as to change its gain, overall negative feedback can not be applied to the gain-controlled amplifier. Therefore, conventional gain-controlled amplifiers without negative feedback have a relatively high distortion factor, (2) the operation of the two pairs of the transistors is asymmetrical to each other, i.e., the operation differs depending upon whether the input signal vi is positive or negative. This is understood from the fact that the currents i.sub.1 b and i.sub.2 a which constitute the current i.sub.0 are determined differently, that is, the current i.sub.1 b depends on the PNP type first transistor pair 1, while the current i.sub.2 a depends on the NPN type second transistor pair 2. According to the polarities of the input signal, as seen from the equation (3), the amount of the currents i.sub.1 b and i.sub.2 a varies. Thus, the asymmetrical operation of the gain-controlled amplifier results in a high distortion with even order harmonics, and (3) the disadvantage described in the above (2) is also caused by an asymmetrical control voltage Vc which is defined by a voltage difference between two common-connected bases, to one common-connected bases of which a potential is applied with respect to ground. In this case, since the transistors are used with a low collector-emitter voltage in view of exponential characteristics, the gain of the respective transistors varies to a large extent and hence the effects of the asymmetrical control voltage Vc is enhanced.